Spot for a business meeting in London - club house, hotel lobby, professional space

I am looking for a place to hold an important business meeting for 3-4 people for 1 hour in central London. I don’t have an office and a cafe or a restaurant isn’t appropriate. Preferably something up lifted. Is there a private members club I could possibly access (for a day) or rent a room or reserve a quiet space, or do you know of a discrete hotel lobby where the staff can facilitate for such conversation to be held? No need for electronic/IT equipment, just some privacy or a quiet nook, table with chairs in a quality spot topped with kind staff to welcome and serve a tea.
Thank you in advance for any recommendations!

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Perhaps try one of the Hoxton Hotels? I know they have several rooms and spaces x

How about Mortimer House?